Syllabus Mathematics 3 - (BE03000211) Total Credits = TH / 30 Assessment Pattern and Marks Total Marks Theory Tutorial / Practical ESE (E) PA (M) PA / (I) TW / SL (I) ESE (V) 04 70 30 20 30 50 200 Unit No. Content 1. Fourier Series : Periodic functions, Fourier series of functions of 2 or any other period, Dirichlet’s condition for convergence of Fourier series, Fourier series of even and odd functions, Half-range Fourier series. (Chapter - 1) 2. Partial Differential Equations (PDEs) : Formation of partial differential equations, solution of first order linear and non-linear partial differential equations, Charpit’s method. Solution of homogeneous and nonhomogeneous linear partial differential equations of second and higher order by complementary function and particular integral method, classification of second order linear partial differential equations, method of separation of variables, one-dimensional wave equation and heat equation. (Chapter - 2) 3. Finite Differences and Interpolation : Finite difference operators and their relations, Newton’s forward and backward difference methods, Lagrange’s interpolation method, Inverse interpolation, Newton’s divided difference method. (Chapter - 3) 4. Numerical Differentiation and Integration : Numerical Differentiation : Derivatives using forward difference and backward difference formulae Numerical Integration : Newton-Cotes quadrature formulae, Trapezoidal rule, Simpson’s rules, Gaussian integration, Case studies. (Chapter - 4) 5. Numerical Solution of Ordinary Differential Equations : Picard’s method, Euler’s method, Runge-Kutta 2nd and 4th order method, Case studies. (Chapter - 5) 6. Laplace Transforms : Laplace transform and Inverse Laplace transform, linearity, first shifting theorem (s-shifting), transforms of derivatives and integrals, ODEs, unit step function (Heaviside function), second shifting theorem (t-Shifting), Laplace transform of periodic functions, short impulses, Dirac’s delta function, convolution, integral equations, differentiation and integration of transforms, ODEs with variable coefficients, systems of ODEs. (Chapter - 6)
